Basic properties
Modulus: | \(3234\) | |
Conductor: | \(539\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(35\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{539}(225,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 3234.bp
\(\chi_{3234}(169,\cdot)\) \(\chi_{3234}(379,\cdot)\) \(\chi_{3234}(421,\cdot)\) \(\chi_{3234}(631,\cdot)\) \(\chi_{3234}(757,\cdot)\) \(\chi_{3234}(841,\cdot)\) \(\chi_{3234}(1093,\cdot)\) \(\chi_{3234}(1219,\cdot)\) \(\chi_{3234}(1303,\cdot)\) \(\chi_{3234}(1345,\cdot)\) \(\chi_{3234}(1555,\cdot)\) \(\chi_{3234}(1681,\cdot)\) \(\chi_{3234}(1807,\cdot)\) \(\chi_{3234}(2017,\cdot)\) \(\chi_{3234}(2143,\cdot)\) \(\chi_{3234}(2227,\cdot)\) \(\chi_{3234}(2269,\cdot)\) \(\chi_{3234}(2479,\cdot)\) \(\chi_{3234}(2605,\cdot)\) \(\chi_{3234}(2689,\cdot)\) \(\chi_{3234}(2731,\cdot)\) \(\chi_{3234}(3067,\cdot)\) \(\chi_{3234}(3151,\cdot)\) \(\chi_{3234}(3193,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{35})$ |
Fixed field: | Number field defined by a degree 35 polynomial |
Values on generators
\((1079,199,2059)\) → \((1,e\left(\frac{3}{7}\right),e\left(\frac{2}{5}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(5\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(37\) | \(41\) |
\( \chi_{ 3234 }(1303, a) \) | \(1\) | \(1\) | \(e\left(\frac{1}{35}\right)\) | \(e\left(\frac{19}{35}\right)\) | \(e\left(\frac{11}{35}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{2}{7}\right)\) | \(e\left(\frac{2}{35}\right)\) | \(e\left(\frac{18}{35}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{18}{35}\right)\) | \(e\left(\frac{22}{35}\right)\) |